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Simplifying ln(x4 + -24x2) + -1ln(x2) = 0 Reorder the terms: ln(-24x2 + x4) + -1ln(x2) = 0 (-24x2 * ln + x4 * ln) + -1ln(x2) = 0 (-24lnx2 + lnx4) + -1ln(x2) = 0 Multiply ln * x2 -24lnx2 + lnx4 + -1lnx2 = 0 Reorder the terms: -24lnx2 + -1lnx2 + lnx4 = 0 Combine like terms: -24lnx2 + -1lnx2 = -25lnx2 -25lnx2 + lnx4 = 0 Solving -25lnx2 + lnx4 = 0 Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Factor out the Greatest Common Factor (GCF), 'lnx2'. lnx2(-25 + x2) = 0 Factor a difference between two squares. lnx2((5 + x)(-5 + x)) = 0Subproblem 1
Set the factor 'lnx2' equal to zero and attempt to solve: Simplifying lnx2 = 0 Solving lnx2 = 0 Move all terms containing l to the left, all other terms to the right. Simplifying lnx2 = 0 The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.Subproblem 2
Set the factor '(5 + x)' equal to zero and attempt to solve: Simplifying 5 + x = 0 Solving 5 + x = 0 Move all terms containing l to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + x = 0 + -5 Combine like terms: 5 + -5 = 0 0 + x = 0 + -5 x = 0 + -5 Combine like terms: 0 + -5 = -5 x = -5 Add '-1x' to each side of the equation. x + -1x = -5 + -1x Combine like terms: x + -1x = 0 0 = -5 + -1x Simplifying 0 = -5 + -1x The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.Subproblem 3
Set the factor '(-5 + x)' equal to zero and attempt to solve: Simplifying -5 + x = 0 Solving -5 + x = 0 Move all terms containing l to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + x = 0 + 5 Combine like terms: -5 + 5 = 0 0 + x = 0 + 5 x = 0 + 5 Combine like terms: 0 + 5 = 5 x = 5 Add '-1x' to each side of the equation. x + -1x = 5 + -1x Combine like terms: x + -1x = 0 0 = 5 + -1x Simplifying 0 = 5 + -1x The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined. The solution to this equation could not be determined.
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